Personally I think that the classic layout used for metro lines/ public trasport systems could work much more for a map like the one you want to develop.
There should be a reason if everyone use this system:
Forget the city layout....go with something classic.
Then to add some nice graphics, you can add some monuments or famous touristic places to the map, etc etc etc
A friend of mine has been in Lisbon recently and he showed to me many pics with interesting places....
Said that I would go with the classic metro graphic layout.
Nobodies